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[ Problem View ]

Measurements in Electric Circuits

Description: Several questions related to a single-loop circuit with one resistor, an ammeter, and a voltmeter. These devices are not necessarily considered ideal. The students are not assumed to know the rules for series and parallel circuits; however, they can make qualitative determinations.

Learning Goal: To understand the role of the internal resistance of various devices and the use of the ammeter and the voltmeter.

Consider the circuit shown. All wires are considered ideal; that is, they have zero resistance. We will assume for now that all other elements of the circuit are ideal, too:

The value of resistance is a constant, the internal resistances of the battery ( ) and

the ammeter ( ) are zero, and the internal resistance of the voltmeter ( ) is

infinitely large.

Part A

What is the reading of the voltmeter?

Express your answer in terms of the EMF .

ANSWER: = EMF

Part B

The voltmeter, as can be seen in the figure, is connected to points 1 and 3. What are the respective voltages between points 1 and 2 and between points 2 and 3?

ANSWER:

Part C

What is the reading of the ammeter?

Express your answer in terms of and .

ANSWER: = EMF/R

To make things more interesting, we now assume that the battery has a nonzero internal

resistance (the voltmeter and the ammeter remain ideal).

Part D

What is the reading of the ammeter now?

Express your answer in terms of , , and .

ANSWER: = EMF/(R+R_int)

Part E

What is the reading of the voltmeter now?

Hint E.1

Hint not displayed

Express your answer in terms of , , and .

ANSWER: = EMF*R/(R+R_int)

Now assume that the ammeter has nonzero resistance . The battery still has nonzero internal resistance.

Part F

Compared to their values when , how would the readings of the ammeter and

the voltmeter change when ?

Hint F.1 How to approach this part

Hint not displayed

ANSWER: The ammeter reading would increase; the voltmeter reading would stay the same.

The ammeter reading would decrease; the voltmeter reading would stay the same.

The ammeter reading would decrease; the voltmeter reading would increase.

The ammeter reading would increase; the voltmeter reading would increase.

Part G

What is the new reading of the ammeter?

Express your answer in terms of , , , and .

ANSWER: = EMF/(R+R_A+R_int)

Now assume that the ammeter again has zero resistance, but the resistance of the voltmeter is less than infinity. The battery still has nonzero internal resistance.

Part H

Compared to their values when , how would the readings of the ammeter and

the voltmeter change when is some large but finite value?

Hint H.1 Consider the voltmeter first

Observe that , where is the current flowing through the battery. What

happens to the current when the resistance of the voltmeter drops?

Hint H.2 The change in the battery current

When the resistance of the voltmeter drops below infinity, it becomes possible for current to flow both through the voltmeter and through the resistor. The overall resistance of the circuit therefore drops, and the current through the battery increases. How would that affect the reading of the voltmeter?

Hint H.3 The reading of the ammeter

The ammeter reading is related simply to the voltmeter reading. The current through

the ammeter is given by , where is the voltage between points 1 and 3, which is exactly the voltage that the voltmeter reads.

ANSWER: The voltmeter reading would stay the same; the ammeter reading would increase.

The voltmeter reading would stay the same; the ammeter reading would decrease.

The voltmeter reading would decrease; the ammeter reading would decrease.

The voltmeter reading would increase; the ammeter reading would increase.

Suppose now that the piece of ideal wire between points 1 and 2 is removed and replaced by a nonideal wire with a nonzero resistance.

Part I

How would this change affect the readings of the ammeter and the voltmeter?

Hint I.1

Hint not displayed

ANSWER: The ammeter reading would stay the same; the voltmeter reading would stay the same.

The ammeter reading would decrease; the voltmeter reading would decrease.

The ammeter reading would increase; the voltmeter reading would decrease.

The ammeter reading would decrease; the voltmeter reading would increase.

The ammeter reading would increase; the voltmeter reading would increase.

The ammeter reading would stay the same; the voltmeter reading would increase.

[ Print ]

2: 0.1270

3: [ Problem View ]

Brightness of Light Bulbs

Description: Asks students to rank brightness of light bulbs in amixed series and parallel circuit.

Consider a circuit containing five identical lightbulbs and an ideal battery.

Part A

Rank the brightness of the five bulbs (A through E) from brightest to dimmest. (The more current flowing through a bulb, the brighter it will be.)

Hint A.1 Comparing bulb A to bulb B

Hint not displayed

Hint A.2 Comparing bulb D to bulb E

Hint not displayed

Hint A.3 Comparing bulb C to bulb D or E

Hint not displayed

Hint A.4 Comparing bulb C to bulb A or B

Hint not displayed

List the bulbs in order from brightest to dimmest. Between each pair of bulbs, use the symbol > to indicate that the left-hand bulb is brighter than the right-hand bulb, or = to indicate that the bulbs have the same brightness. For example, "B=C=E>A>D" means that bulbs B, C, and E all have the same brightness, and that they are brighter than bulb A, which in turn is brighter than bulb D.

ANSWER: C>A=B>D=E

C>A=B>E=D

C>B=A>D=E

C>B=A>E=D

Now consider what happens when a switch in the circuit is opened.

Part B

What happens to bulb A?

Hint B.1 How to approach this part

How does the resistance of bulb C alone compare with the resistance of bulb C in parallel with bulbs D and E?How does this affect the resistance and current in the circuit as a whole (as compared

to before)?

ANSWER: It gets dimmer.

It gets brighter.

Its brightness stays the same.

Part C

What is the current now flowing in bulb C?

Express your answer in terms of the applied voltage and , the resistance of a single bulb.

ANSWER: = (2*EMF)/(3*R)

Part D

What happens to bulb C?

Part D.1 Current in bulb C earlier

The total resistance of the earlier circuit was , where is the resistance of one

bulb. What is the current flowing in bulb C?

Express your answer in terms of and .

ANSWER:Answer not displayed

ANSWER: It gets dimmer.

It gets brighter.

Its brightness stays the same.

This is why appliances in your home are connected only in parallel. Otherwise, turning some on or off would cause the current in others to change, which could damage them (typically in the case of an overload) or prevent them from functioning (if the current is too low).

[ Print ]

4. [ Problem View ]

Batteries in Series or Parallel

Description: Computation of current through a resistor for parallel and series connected

batteries.

You are given two circuits with two batteries of emf and internal resistance each.

Circuit A has the batteries connected in series with a resistor of resistance , and circuit B has the batteries connected in parallel to an equivalent resistor.

Note that the symbol should be entered in your answers as EMF.

Part A

In which direction does the current in circuit A flow?

Hint A.1 Conventions

Remember that the conventional current flows from a positive to a negative terminal.

ANSWER: clockwise counterclockwise

Part B

What is the current through the resistor of resistance in circuit A?

Hint B.1

Hint not displayed

Hint B.2

Hint not displayed

Express the current in terms of , , and .

ANSWER: =

2*EMF/(2*R_1+R_2)

2*E/(2*R_1+R_2)

Part C

Calculate the current through the resistor of resistance for circuit B.

Hint C.1 Which rule to use

Hint not displayed

Part C.2 What is the emf for loop 1?

The diagram shows the circuit divided into two loops: is the current in the topmost

branch, is the current in the branch below it, while is the current in the

lowest branch, which contains . Find an expression for the emf using the voltage drops across the two resistors in loop 1.

Express your answer in terms of , , , and .

ANSWER: = I_3*R_2+I_1*R_1

Part C.3 What is the emf for loop 2?

Part not displayed

Part C.4 Application of Kirchhoff's junction rule (current rule)

You should now have two equations involving all the variables in the circuit diagram.

To solve for , you need a relationship between and . Choose the correct relation by applying Kirchhoff's junction rule to one of the junctions. Recall that Kirchhoff's junction rule states that the algebraic sum of all the currents into a junction is zero:

.

ANSWER:

Now solve the three equations you have obtained for the currents in each branch to

obtain an expression for ( ). To do this, you could either add the two equations

other than the one above, or substitute for and from the other equations into this one.

Express your answer in terms of , , and .

ANSWER: =

2*EMF/(2*R_2+R_1)

2*E/(2*R_2+R_1)

Part D

What is the power dissipated by the resistor of resistance for circuit A, given that

, , and ?

Hint D.1 What formula to use

Hint not displayed

Calculate the power to two significant figures.

ANSWER: = 6.40×10-2 W

Part E

For what ratio of and would power dissipated by the resistor of resistance be

the same for circuit A and circuit B?

Hint E.1

Hint not displayed

Hint E.2

Hint not displayed

ANSWER: = 1.00

Part F

Under which of the following conditions would power dissipated by the resistance in circuit A be bigger than that of circuit B?

Hint F.1 How to think about the problem

Hint not displayed

Some answer choices overlap; choose the most restrictive answer.

ANSWER:

[ Print ]

5.zeroemfclockwisetop plate zero

=C*EMF

=EMF^2*C

=C*EMF*(1-exp(-t/(R*C)))

=EMF/R*exp(-t/(R*C)) =9.21*tau =5.530×10-2

=q_0*exp(-t/(R*C))

=-q_0/(R*C)*exp(-t/(R*C))

6. =(epsilon_0*r^2/d*(K-1)*V)/DeltaT

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